NONLINEAR DYNAMICS in VERTICAL-CAVITY SURFACE-EMITTING LASERS

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					 NONLINEAR DYNAMICS in
    VERTICAL-CAVITY
SURFACE-EMITTING LASERS

   Krassimir Panajotov
     Ignace Gatare

    Marc Sciamanna
                           5 COST 288
                            countries
       Angel Valle

    Wolfgang Elsaßer
                         kpanajotov@tona.vub.ac.be
 NONLINEAR DYNAMICS in VCSELs



Optical injection;
Unidirectional synchronization;
Optical Feedback;
Gain Switching;
Spatio-temporal dynamics and
Cavity Solitons

                                  kpanajotov@tona.vub.ac.be
 NONLINEAR DYNAMICS in VCSELs



Optical injection;
Unidirectional synchronization;
Optical Feedback;
Gain Switching;
Spatio-temporal dynamics and
Cavity Solitons

                                  kpanajotov@tona.vub.ac.be
                 Setup for optical injection




Slave: oxide confined GaAs/AlGaAs VCSEL emitting at 845 nm;
       threshold ~1 mA, birefringence splitting ~ 2 GHz

Master: tunable EC laser (Littrow configuration), polarization turned to be
orthogonal to that of the slave VCSEL light

Isolators to prevent OF from detection part, and to ensure unidirectional
coupling
I. Gatare et al, Appl. Phys. Lett., 88, 101106 (2006)     kpanajotov@tona.vub.ac.be
   PS induced by OI: hysteresis properties

                                                   Free-running VCSEL:
                                                   polarization resolved
                                                   L-I curves




When the VCSEL is monostable, OI leads   When the VCSEL is bistable, the
to PS with hysteresis                    VCSEL keeps the master
                                         polarization when OI is off




                                                      kpanajotov@tona.vub.ac.be
            Mapping of polarization dynamics

                                                              S: injection locking
                                                              U: unlocking
                                                              B: bistable PS
                                                              C: chaos
                                                              PD: period doubling


                                                              → Route to
                                                              bistable PS (B) may
                                                              be accompanied by
                                                              injection locking (S)
                                                              but also by complex
                                                              dynamics (C)




J. Buesa et al, IEEE Jour. Quant. Electr., 42, 198 (2006)   kpanajotov@tona.vub.ac.be
Mapping of Pol.dynamics: PS+locking and
PD route to chaos




∆ω = -10 GHz
                               ∆ω = 2 GHz
(a) – (b): PS with injection
                               (a) PS with injection locking; (b) Hopf
locking followed by Hopf
                               bifurcation to limit cycle (LC) at RO
bifurcation (c) to period-
                               frequency; (c) harmonics; (d) period
one limit cycle (d)
                               doubling; (e) chaos, (f) reverse period
                               doubling, (g), (h) limit cycle period one
                                                 kpanajotov@tona.vub.ac.be
           Bistable polarization switching –
           underlying bifurcations
 Initial condition: slave VCSEL with only x-LP mode stable, biased at µ = 1.5
 (before a PS point to y-LP mode)




                                                   C



                                                                IL
                                           A bifurcation diagram unveils a
Evolution of the mean x and y              cascade of bifurcations to
intensities with injection strength:       complex dynamics in the two
PS and bistability                         polarization modes (period
                                           doubling route to chaos)
                                                           kpanajotov@tona.vub.ac.be
      VCSEL with OI:
results from SFM model (1)
             Rich nonlinear dynamics!

              Saddle-node (SN), Hopf (H1 & H2)
           bifurcations delimit the region of stable
           injection locking

              PS points interplay with bifurcation
           curves, with a min injection power needed
           for PS located on H2 bifurcation

              PD bifurcations to chaos appear close
           to these local min in the PS curve, as in
           experiments

              A Torus bifurcation explains the time-
           periodic polarization dynamics before PS
           & locking observed experimentally


                               kpanajotov@tona.vub.ac.be
Nonlinear Dynamics in VCSELs with Optical
Feedback: Pulse Packages

VCSEL
             τ




T. Heil, I. Fisher, W. Elsäßer and A. Gavrielides, Phys. Rev. Lett., 87, 243901 (2001)
                                                              kpanajotov@tona.vub.ac.be
Polarization Mode Competition in PP regime

                                             I=3.2 mA




                                             I=3.4 mA




                                             I=3.8 mA




                                             I=5.0 mA



                             kpanajotov@tona.vub.ac.be
Polarization Mode Competition:
  as a function of injection current


    Correlated           Polarization mode
     behavior
                         suppression ratio
              Anti-      of Solitary VCSEL
           Correlated
            behavior




                              kpanajotov@tona.vub.ac.be
        List of joint publications acknowledging COST 288 action

1. J. Buesa, I. Gatare, K. Panajotov, H. Thienpont, and M. Sciamanna,
Mapping of the Dynamics Induced by Orthogonal Optical Injection in VCSELs,
IEEE Journ. Quant. Electr., 42, 198-207, 2006.

2. A. Tabaka, M. Peil, M. Sciamanna, I. Fischer, W. Elsaßer, H. Thienpont, I.
Veretennicoff, K. Panajotov,
Dynamics of VCSELs in the Short External Cavity Regime: Pulse Packages and
Polarization Mode Competition,
Phys. Rev. A, 73, 13810, 2006.

3. I. Gatare, M. Sciamanna, J. Buesa, H. Thienpont, K. Panajotov,
Nonlinear dynamics accompanying polarization switching in VCSELs with orthogonal
optical injection,
Appl. Phys. Lett., 88, 101106, 2006.

4. M. Sciamanna, K. Panajotov,
Route to polarization switching induced by optical injection in vertical-cavity surface-
emitting lasers,
Phys. Rev. A, 73, 023811, 2006                                     kpanajotov@tona.vub.ac.be
5. I. Gatare, K. Panajotov, M. Sciamanna,
Frequency-induced polarization bistability in VCSELs with orthogonal optical injection,
Phys. Rev. A, 75, 023804, 2007.

6. A. Valle, I. Gatare, K. Panajotov, M. Sciamanna,
Transverse mode switching and locking in VCSELs subject to Orthogonal
Optical Injection,
IEEE Journ. Quant. Electr, 43, 322, 2007.

7. M. Sciamanna, I. Gatare, A. Locquet, K. Panajotov,
Polarization synchronization in unidirectionally coupled VCSELs,
Phys. Rev. E, 75, 056213, 2007.

8. I. Gatare, M. Sciamanna, A. Locquet, K. Panajotov,
Influence of polarization mode competition on the synchronization of two
unidirectionally coupled VCSELs,
Opt. Lett., 32, 1629, 2007.


                                                               kpanajotov@tona.vub.ac.be

				
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